A search is presented for narrow heavy resonances X decaying into pairs of Higgs bosons (H) in proton-proton collisions collected by the CMS experiment at the LHC at sqrt(s) = 8 TeV. The data correspond to an integrated luminosity of 19.7 inverse femtobarns. The search considers HH resonances with masses between 1 and 3 TeV, having final states of two b quark pairs. Each Higgs boson is produced with large momentum, and the hadronization products of the pair of b quarks can usually be reconstructed as single large jets. The background from multijet and t t-bar events is significantly reduced by applying requirements related to the flavor of the jet, its mass, and its substructure. The signal would be identified as a peak on top of the dijet invariant mass spectrum of the remaining background events. No evidence is observed for such a signal. Upper limits obtained at 95% confidence level for the product of the production cross section and branching fraction sigma(gg to X) B(X to HH to b b-bar b b-bar) range from 10 to 1.5 fb for the mass of X from 1.15 to 2.0 TeV, significantly extending previous searches. For a warped extra dimension theory with a mass scale Lambda[R] = 1 TeV, the data exclude radion scalar masses between 1.15 and 1.55 TeV.